Bifurcations to Periodic Solutions in a Production/Inventory Model

Total production costs show sometimes an S-shaped form. There are several ways in which a plant with given capacity can be adapted to a specific demand rate, one of them being adaptation of intensity per work hour. In this paper we present an application of the Hamilton-Hopf bifurcation to an inventory/production intensity splitting model with a nonconvex cost function. Our analysis provides a new proof that persistent oscillations may be optimal for arbitrary small discount rates. For zero discounting a “Hamilton Hopf bifurcation” occurs, leading to a family of periodic solutions bifurcating from a steady state. If the discount rate becomes positive, almost all periodic solutions vanish; only an unique branch of periodic solutions is obtained. Date: December 23, 2003. 1 2 A. STEINDL AND G. FEICHTINGER